Can I read Network Goodness-of-Fit for the block-model family on EtoBox?

Network Goodness-of-Fit for the block-model family by Jin, Jiashun; Ke, Zheng Tracy; Tang, Jiajun; Wang, Jingming is a scholarly article available to read on EtoBox.

What is Network Goodness-of-Fit for the block-model family about?

The block-model family has four popular network models (SBM, DCBM, MMSBM, and DCMM). A fundamental problem is, how well each of these models fits with real networks. We propose GoF-MSCORE as a new Goodness-of-Fit (GoF) metric for DCMM (the broadest one among the four), with two main ideas. The first is to use cycle count statistics as a general recipe for GoF. The second is a novel network fitting scheme. GoF-MSCORE is a flexible GoF approach, and we further extend it to SBM, DCBM, and MMSBM. This gives rise to a series of GoF metrics covering each of the four models in the block-model family. We show that for each of the four models, if the assumed model is correct, then the corresponding GoF metric converges to $N(0, 1)$ as the network sizes diverge. We also analyze the powers and show that these metrics are optimal in many settings. In comparison, many other GoF ideas face challenges: they may lack a parameter-free limiting null, or are non-optimal in power, or face an analytical hurdle. Note that a parameter-free limiting null is especially desirable as many network models have a large number of unknown parameters. The limiting nulls of our GoF metrics are always $N(0,1)$, whic

Author

Jin, Jiashun; Ke, Zheng Tracy; Tang, Jiajun; Wang, Jingming

Published

2025

Language

EN